Download 2017_53: Radiation, reflection and breakdown of

2017_53: Radiation, reflection and breakdown of
Rossby waves and their role in stratospheretroposphere coupling
Supervisors: Professor Xuesong Wu ([email protected]), Dr Pavel Berloff
(Mathematics)
Department: Department of Mathematics
We will conduct a systematic theoretical study of radiation, reflection and breakdown
of Rossby waves in rotating shear flows that are characteristic of the atmospheric
boundary layer in the troposphere and zonal jets in the stratosphere. Typically, there
exists a critical level, where the base flow velocity equals the phase speed of the wave.
The emphasis of our investigation will be on nonlinear effects, which become
significant in the so-called critical layer, i.e. a relatively thin region surrounding the
critical level.
For radiation of Rossby waves, two mechanisms will be considered. The first is the
direct emission of Rossby waves by the so-called radiating instability modes with fairly
long wavelengths, and our aim is to describe analytically the emitted Rossby wave in
the far field when a wavepacket of the mode undergoes nonlinear evolution. The
second mechanism is the radiation due to the nonlinear interaction of shortwavelength instability modes trapped in the shear layer, a process involving
backscattering of the disturbance energy. The reflection problem is to be formulated
pertaining to the stratosphere, and we shall consider the case where the incident wave
is strong enough that the dynamics in the critical layer is strongly nonlinear, and the
reflected and transmitted signals consist of all nonlinearly-generated harmonics. We
will analyse wave breakdown, which may occur in the form of overturning, or via a
secondary local instability, which leads to rapid amplification of small-scale
fluctuations.
The insights gained for these three fundamental processes will be applied to improve
the modelling of the forcing of Rossby waves on the stratosphere. However, our
primary interest will be in the two-way coupling between the troposphere and
stratosphere via the Rossby waves emitted from the former and then reflected back
from the latter. A mathematical theory will be formulated by using a multi-scale
approach.
For more information on how to apply visit us at www.imperial.ac.uk/changingplanet